1.6. Eratosthenes noticed that the shadow's length was 1/8 the pole's height. Suppose the pole's height was h = 2 m and the shadow's length was l = 0.25 m. Calculate the angle between the Sun's ray and the pole's axis in degrees: $ = Express the same angle in radians: o =, 1.7. Recall the beam of light travelling down the well in Syene. Extend that beam to the center of Earth. Also extend the pole's axis to the center of Earth. These two extensions are represented by dashed lines in Figure 1. The intersection of these two lines forms an angle 0 at the Earth's center. Use basic geometry to find the relation between angles O and p. Calculate the angle 0 in radians: 0 =, 1.8. Having access to the vast informational resources of the Library of Alexandria, Eratosthenes knew that the distance between Syene and Alexandria is 5000 stadia. One stadion (plural stadia) was a unit of length commonly used at the time; it was approximately equal to 160 meters. Express the distance between Syene and Alexandria in meters: s = 1.9. Travelling from Syene to Alexandria, one travels along the arc of a circle. Recall that for a circle of radius R, the length s of an arc and the angle 0 subtended by that arc are related by the following equation: s = R O In using this equation, the angle must be measured in radians. Use equation [8] to [8] calculate the radius of Earth: R =. 1.10.As it turns out, Earth is not exactly spherical due to its daily rotation and the gravitational pull of the Moon. Thus, Earth's radius at the equator is slightly larger than its radius at the north pole. A good average value for the Earth's radius, consistent with modern measurements, is 6,371,000 m. Scientific experiments often involve comparing a measured or observed value to a calculated or expected value. The best way to do this is to calculate the percent difference: Measured – Expected % Difference = х 100% [9] Expected
1.6. Eratosthenes noticed that the shadow's length was 1/8 the pole's height. Suppose the pole's height was h = 2 m and the shadow's length was l = 0.25 m. Calculate the angle between the Sun's ray and the pole's axis in degrees: $ = Express the same angle in radians: o =, 1.7. Recall the beam of light travelling down the well in Syene. Extend that beam to the center of Earth. Also extend the pole's axis to the center of Earth. These two extensions are represented by dashed lines in Figure 1. The intersection of these two lines forms an angle 0 at the Earth's center. Use basic geometry to find the relation between angles O and p. Calculate the angle 0 in radians: 0 =, 1.8. Having access to the vast informational resources of the Library of Alexandria, Eratosthenes knew that the distance between Syene and Alexandria is 5000 stadia. One stadion (plural stadia) was a unit of length commonly used at the time; it was approximately equal to 160 meters. Express the distance between Syene and Alexandria in meters: s = 1.9. Travelling from Syene to Alexandria, one travels along the arc of a circle. Recall that for a circle of radius R, the length s of an arc and the angle 0 subtended by that arc are related by the following equation: s = R O In using this equation, the angle must be measured in radians. Use equation [8] to [8] calculate the radius of Earth: R =. 1.10.As it turns out, Earth is not exactly spherical due to its daily rotation and the gravitational pull of the Moon. Thus, Earth's radius at the equator is slightly larger than its radius at the north pole. A good average value for the Earth's radius, consistent with modern measurements, is 6,371,000 m. Scientific experiments often involve comparing a measured or observed value to a calculated or expected value. The best way to do this is to calculate the percent difference: Measured – Expected % Difference = х 100% [9] Expected
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Concept explainers
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
Topic Video
Question
100%
![1.6. Eratosthenes noticed that the shadow's length was 1/8 the pole's height. Suppose the
pole's height was h = 2 m and the shadow's length was l = 0.25 m. Calculate the angle
between the Sun's ray and the pole's axis in degrees: $ =
Express
the same angle in radians: =,
1.7. Recall the beam of light travelling down the well in Syene. Extend that beam to the
center of Earth. Also extend the pole's axis to the center of Earth. These two extensions
are represented by dashed lines in Figure 1. The intersection of these two lines forms
an angle 0 at the Earth's center. Use basic geometry to find the relation between angles
O and p. Calculate the angle 0 in radians: 0 =
1.8. Having access to the vast informational resources of the Library of Alexandria,
Eratosthenes knew that the distance between Syene and Alexandria is 5000 stadia. One
stadion (plural stadia) was a unit of length commonly used at the time; it was
approximately equal to 160 meters. Express the distance between Syene and
Alexandria in meters: s =
1.9. Travelling from Syene to Alexandria, one travels along the arc of a circle. Recall that for
a circle of radius R, the length s of an arc and the angle 0 subtended by that arc are
related by the following equation:
s = R O
In using this equation, the angle must be measured in radians. Use equation [8] to
[8]
calculate the radius of Earth: R =,
1.10. As it turns out, Earth is not exactly spherical due to its daily rotation and the gravitational
pull of the Moon. Thus, Earth's radius at the equator is slightly larger than its radius at
the north pole. A good average value for the Earth's radius, consistent with modern
measurements, is 6,371,000 m. Scientific experiments often involve comparing a
measured or observed value to a calculated or expected value. The best way to do this
is to calculate the percent difference:
Measured – Expected
% Difference =
× 100%
[9]
Expected](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87082b8a-b4f5-455e-a232-6f60990eaa64%2Fd5e749cf-9c7e-4228-b437-01693fe0f615%2Ff7uuy99_processed.png&w=3840&q=75)
Transcribed Image Text:1.6. Eratosthenes noticed that the shadow's length was 1/8 the pole's height. Suppose the
pole's height was h = 2 m and the shadow's length was l = 0.25 m. Calculate the angle
between the Sun's ray and the pole's axis in degrees: $ =
Express
the same angle in radians: =,
1.7. Recall the beam of light travelling down the well in Syene. Extend that beam to the
center of Earth. Also extend the pole's axis to the center of Earth. These two extensions
are represented by dashed lines in Figure 1. The intersection of these two lines forms
an angle 0 at the Earth's center. Use basic geometry to find the relation between angles
O and p. Calculate the angle 0 in radians: 0 =
1.8. Having access to the vast informational resources of the Library of Alexandria,
Eratosthenes knew that the distance between Syene and Alexandria is 5000 stadia. One
stadion (plural stadia) was a unit of length commonly used at the time; it was
approximately equal to 160 meters. Express the distance between Syene and
Alexandria in meters: s =
1.9. Travelling from Syene to Alexandria, one travels along the arc of a circle. Recall that for
a circle of radius R, the length s of an arc and the angle 0 subtended by that arc are
related by the following equation:
s = R O
In using this equation, the angle must be measured in radians. Use equation [8] to
[8]
calculate the radius of Earth: R =,
1.10. As it turns out, Earth is not exactly spherical due to its daily rotation and the gravitational
pull of the Moon. Thus, Earth's radius at the equator is slightly larger than its radius at
the north pole. A good average value for the Earth's radius, consistent with modern
measurements, is 6,371,000 m. Scientific experiments often involve comparing a
measured or observed value to a calculated or expected value. The best way to do this
is to calculate the percent difference:
Measured – Expected
% Difference =
× 100%
[9]
Expected
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON